Abstract
We develop optimal respiratory airflow patterns using a nonlinear multicompartment model for a lung mechanics system. Specifically, we use classical calculus of variations minimization techniques to derive an optimal airflow pattern for inspiratory and expiratory breathing cycles. The physiological interpretation of the optimality criteria used involves the minimization of work of breathing and lung volume acceleration for the inspiratory phase, and the minimization of the elastic potential energy and rapid airflow rate changes for the expiratory phase. Finally, we numerically integrate the resulting nonlinear two-point boundary value problems to determine the optimal airflow patterns over the inspiratory and expiratory breathing cycles.
Highlights
Respiratory failure, the inadequate exchange of carbon dioxide and oxygen by the lungs, is a common clinical problem in critical care medicine, and patients with respiratory failure frequently require support with mechanical ventilation while the underlying cause is identified and treated
The purpose of our work in this paper is to provide a mathematically rigorous and general framework developing optimal determination of respiratory airflow patterns using a nonlinear multicompartment model for a lung mechanics system
We extend the work of [17, 18] to develop optimal respiratory airflow patterns using a nonlinear multicompartment model for a lung mechanics system. (The usage of the word optimal throughout the paper refers to an optimal solution of the calculus of variations problems addressed in the paper and not an optimal breathing pattern in the sense of respiratory physiology.) First, we extend the linear multicompartment lung model given in [6] to address system model nonlinearities
Summary
Respiratory failure, the inadequate exchange of carbon dioxide and oxygen by the lungs, is a common clinical problem in critical care medicine, and patients with respiratory failure frequently require support with mechanical ventilation while the underlying cause is identified and treated. For adaptive control of mechanical ventilation, that is, more advanced controller architectures than simple volume- or pressure-controlled ventilation, more elaborate models are needed, especially when accounting for nonlinear compliance and resistance and lung heterogeneity [6]. The purpose of our work in this paper is to provide a mathematically rigorous and general framework developing optimal determination of respiratory airflow patterns using a nonlinear multicompartment model for a lung mechanics system. We extend the work of [17, 18] to develop optimal respiratory airflow patterns using a nonlinear multicompartment model for a lung mechanics system. We write (·)T to denote transpose, (·) to denote Frechet derivative, and δx to denote the first variation of the function x
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